The prices of two fruits sold at a supermarket is shown.
| Fruit |
Price |
| Kiwis |
3 kg for $7 |
| Peaches |
6 kg for $3 |
- Tommy bought an equal mass of kiwis and peaches and spent $22 more on kiwis than on peaches. What was the total mass of fruits that Tommy bought?
- Opal spent an equal amount of money on kiwis and peaches. In terms of their masses, what was the ratio of kiwis to the ratio of peaches Opal bought?
(a)
LCM of 3 and 6 = 6
One set = 6 kg of kiwis and 6 kg of peaches
Number of sets of 3 kg of kiwis
= 6 ÷ 3
= 2
Number of sets of 6 kg of peaches
= 6 ÷ 6
= 1
Difference in price of kiwis and peaches in one set
= 2 x 7 - 1 x 3
= 14 - 3
= $11
Number of sets
= 22 ÷ 11
= 2
Mass of kiwis and peaches in one set
= 6 + 6
= 12 kg
Total mass of fruits bought
= 2 x 12
= 24 kg
(b)
LCM of 7 and 3 = 21
Number of sets of 3 kg of kiwis to be bought with $21
= 21 ÷ 7
= 3
Mass of 3 sets of 3 kg of kiwis
= 3 x 3
= 9 kg
Number of sets of 6 kg of kiwis to be bought with $21
= 21 ÷ 3
= 7
Mass of 7 sets of 6 kg of peaches
= 7 x 6
= 42 kg
Mass of kiwis : Mass of peaches
9 : 42
(÷3) 3 : 14
Answer(s): (a) 24 kg; (b) 3 : 14
